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{
    "pk": 64959,
    "title": "Permutoric promotion: gliding globs, sliding stones, and colliding coins",
    "subtitle": null,
    "abstract": "Defant recently introduced toric promotion, an operator that acts on the labelings of a graph \\(G\\) and serves as a cyclic analogue of Schützenberger's promotion operator. Toric promotion is defined as the composition of certain toggle operators, listed in a natural cyclic order. We consider more general permutoric promotion operators, which are defined as compositions of the same toggles, but in permuted orders. We settle a conjecture of Defant by determining the orders of all permutoric promotion operators when \\(G\\) is a path graph. In fact, we completely characterize the orbit structures of these operators, showing that they satisfy the cyclic sieving phenomenon. The first half of our proof requires us to introduce and analyze new broken promotion operators, which can be interpreted via globs of liquid gliding on a path graph. For the latter half of our proof, we reformulate the dynamics of permutoric promotion via stones sliding along a cycle graph and coins colliding with each other on a path graph.\n \nMathematics Subject Classifications: 05E18\n \nKeywords: Promotion, toric promotion, Coxeter element, cyclic sieving phenomenon",
    "language": "en",
    "license": {
        "name": "Creative Commons Attribution 4.0",
        "short_name": "CC BY 4.0",
        "text": "Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.\n\nNo additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.",
        "url": "https://creativecommons.org/licenses/by/4.0"
    },
    "keywords": [
        {
            "word": "Promotion"
        },
        {
            "word": "toric promotion"
        },
        {
            "word": "Coxeter element"
        },
        {
            "word": "cyclic sieving phenomenon"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/71r9p20q",
    "frozenauthors": [
        {
            "first_name": "Colin",
            "middle_name": "",
            "last_name": "Defant",
            "name_suffix": "",
            "institution": "Department of Mathematics, Harvard University, Cambridge, MA 02139, U.S.A.",
            "department": ""
        },
        {
            "first_name": "Rachana",
            "middle_name": "",
            "last_name": "Madhukara",
            "name_suffix": "",
            "institution": "Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A.",
            "department": ""
        },
        {
            "first_name": "Hugh",
            "middle_name": "",
            "last_name": "Thomas",
            "name_suffix": "",
            "institution": "Lacim, UQAM, Montréal, QC, H3C 3P8, Canada",
            "department": ""
        }
    ],
    "date_submitted": "2024-09-27T11:38:15+02:00",
    "date_accepted": "2024-09-27T11:38:15+02:00",
    "date_published": "2024-09-30T09:00:00+02:00",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64959/galley/49769/download/"
        }
    ]
}